Gonihedric 3D Ising Actions

Abstract

We investigate a generalized Ising action containing nearest neighbour, next to nearest neighbour and plaquette terms that has been suggested as a potential string worldsheet discretization on cubic lattices by Savvidy and Wegner. We use both mean field techniques and Monte-Carlo simulations to sketch out the phase diagram. The Gonihedric (Savvidy-Wegner) model has a symmetry that allows any plane of spins to be flipped with zero energy cost, which gives a highly degenerate vacuum state. We choose boundary conditions in the simulations that eliminate this degeneracy and allow the definition of a simple ferromagnetic order parameter. This in turn allows us to extract the magnetic critical exponents of the system.

Comments: Latex plus 6 postscript figures bundled together with uufiles. The paper has been completely revised: a judicious choice of boundary conditions now allows the extraction of magnetic critical exponents. All the exponents, and even the critical temperature, appear close to those of the standard two-dimensional Ising model